Two taps used alternately — Time & Work Aptitude Question
Two taps used alternately: Tap A fills a tank in 4 hours and tap B in 6 hours. They are opened alternately for one… Answer and worked solution on CodeKairo.
- Topic: Time & Work
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 135 seconds
Question
Tap A fills a tank in 4 hours and tap B in 6 hours. They are opened alternately for one hour each, starting with A. How long does the tank take to fill?
Options
- 4 h 20 min
- 4 h 40 min
- 5 h
- 5 h 20 min
Show the answer and the worked solution
Correct answer: B. 4 h 40 min
Worked solution
- Tank = 12 units. A adds 3 units/hour, B adds 2.
- Each 2-hour cycle adds 5 units. After 2 cycles (4 hours): 10 units.
- The 5th hour is A's turn; he needs 2 more units at 3 units/hour = 2/3 hour = 40 minutes.
- Total = 4 h 40 min.
Answer: 4 h 40 min.
The idea
Count whole cycles first, then finish the remainder with whoever's turn it is. The remainder rarely takes a full period, so express it in minutes.
Shortcut. In 12 units, every A-then-B pair of hours adds 5, so after 4 hours 2 units remain and the turn is A's; 2 of A's 3 units an hour take 40 minutes.
Common trap. 5 h — giving the fifth hour to B, whose 2 units an hour would fill the last 2 units in exactly an hour; A started, so the fifth hour is A's.